Chart for determining the flux of light.



A. A. WOHLAUER.

CHART FOR DETERMINING THE PLUXOF LIGHT.

APPLICATION FILED 111:0. 18, 1908.

1,034,943, Patented Aug. 6,1912.

2 SHEETS-SHEET 1.

WITNESSES V INVENTOR W I zfi olfmi A. A. WOELAUER, {HART FOR DETERMINING TEE FLUX OF LIGHT. APPLICATION FILED D2018, 1908.

2 O 34 943 a Patented Aug; 6, 1912.

2 SHEETS-SHEET 2.

ATTORNEYS ALFRED A. WOHLAUEB, OF NEW YORK, N. Y.

CHART FOR DETERMINING THE FLUX OF LIGHT.

Specification of Letters Patent.

Patented Aug. 6, 1912.

Application filed December 18, 1908. Serial No. 468,157.

. a subject of the Emperor of Germany, and

resident of the borough of Manhattan, city, county, and State of New York, have invented certain new and useful Improvements in Charts for Determining the Flux of Light, of which the following is a specification.

My invention relates to charts or ruled sheets for the use of illuminating engineers in solvin problems b the aid of the socalled flux of light met 'od. For the sake of explanation, I will say that the flux of light is defined as the total amount vof radiation issuingfrom a single source oflight or from a number of light sources. This flux of light is generally measured in lum'ens, a

lumen being of the flux of one mean spherical candle and thus equaling the flux required to give one square foot an illumination of one foot. candle.

Problems in illuminatin involve the refiection or distribution of t e available flux of light to secure certain results, such as a uniform average illumination (flux density) of a given surface or area. My improved chart enables such problems to be solved much more readily than any other means or method known to me, and without any complicated calculations.

Figures 1, 2 and 3 of the accompanying drawings illustrate three different charts embodying my invention.

In each case I employ a combination of rectangular and polar coordinates, and in the drawings the chart consists of a series of concentric circles, a number of lines radiating from the center of said circles, and a network of lines crossing each other at right angles and forming squares similar to those of the well-known cross-section paper. In charts embodying my invention, a peculiar definite relation, fully set forth hereinafter, obtains between the angular subdivisions (or in other words, the number of radial lines) and the ratio between the unit of the rectangular coordinates and that of the scale which the circles indicate on the radial lines.

, The charts may be printed or otherwise prothe heavy radial lines A are sectors of 30 each. The thin radial lines B are the median lines or bisectrices of these divisions or sectors. The horizontal lines C (abscissae) which measure the flux in lumens, and the vertical lines D, which indicate the lumens according to the notation or scale E, are evenly spaced, the interval in this particular case corresponding to a half unit. The zero of the scale E corresponds to the center from which the lines A, B radiate. Around this center are described parallel circles F, evenly spaced, the interval between adjacent circles indicating one candle, as shown by the polar candle scale G. The unit interval of the scale G is shown as bearing the ratio 3.25 to the unit interval of the scale E, which is in practice a sufficiently close approximation to the theoretical ratio. Intermediate thinner circles H may be described half-way between the circles F, and of course the degree of subdivision may be varied, both for the rectangular coordinates and for the circles. (It will be seen that the ten units of the scale G occupy a space corresponding to 32.5 units of the scale E.)

The chart Fig. 2 shows semicircles F, instead of the full circles F, H of Fig. 1, and the subdivisions for the radial lines A are shown as 5. With this angle the ratio of the unit of the candle scale G to that of the lumen scale E is .55. The general arrangement of lines and scales is similar to that'of Fig. 1, as may be seen by the reference letters applied to corresponding parts.

Fig. 3 shows still another angular subdivision viz. one-of 9, and also shows the chart extended only through 90. The 9 division has the peculiarity of giving almost equal value to the units of the lumen scale have been shown equal, which in practice is a negligible departure from the theoreti-- cally correct ratio of .99.,

These examples are intended to show that my invention is not limited to any particular angular subdivision, or to any particular extent of the chart. Of the chart shown in Fig. 1, only a portion, say one half or one-fourth, may be sufficient in some cases, and similarly, the charts Figs. 2 and 3 may be extended to the full circle if desired. I wish it to be understood that the term circle as used in the claims, includes semicircles or other circular arcs as well as full circles. In all forms of my invention, however, the unit of the lumen scale bears a definite relation to that of the candle scale, said relation or ratio being a function of the angular subdivision employed. If this angle be 0:, then the said ratio is Y 27: 2 sin.

2 R= =47z S111. 9?.

sin. 52 sin. it 2 W=21rP(cos. a -cos. Q The length of any abscissa is found as a P S111. 5

(see the triangle inclosed by the first two lines A, B of Fig. 1), if a indicates the a Psln.

The median lines B, B, B indicate the flux of light issuing over the angle between the corresponding adjacent lines A, A or A respectively.

A brief example may illustrate the use of my invention. Suppose that, as shown at J in Fig. 1, the polar curve or diagram has been plotted on the chart in the well-known manner. If it is desired to find the flux distribution over the angle from 0 to 60, we proceed as follows: We find the abscissa corresponding to the point of intersection of the polar curve J with the first line B (at 15), which abscissa (found as'1.5) determines the flux over the angle from 0 to 30. Similarly the abscissa of the point of intersection of the polar curve J with the second line B (at 45) measures the flux over the angle from 30 to 60 .(this abscissa is found as, say 12.5). The total flux from 0 to 60 equals the sum of the two fluxes determined as above, that is to say 1.5+12.5=14L lumens.

27:P(1 cos. a) 2n-(l cos. a)

angle of subdivision (30 in Fig. 1). N 0w For equal angles of subdivision, a -oz is constant, and therefore in w is also constant. Therefore the relation of i the fluxes for equal angular subdivisions will be directly proportional to and to the candle power P. For a =0, we have r e; 2 S111. s1n.

showing that the flux is proportional to the abscissae. For a =0, we have W:21cP(1- cos. 0:).

Therefore the ratio R of flux to abscissa, for equal subdivisions, is

sin. 2

being transparent so that when they are superposed, they will constitute together a chart such as herein described. Such a chart, whether-made of one piece or more, I consider as falling withinthe scope of my invention as defined in the claims.

I have explained above that in my improved chart the ratio of the unit of the candle scale G, G, G to the unit of the lumen scale E, E E is equal to a: 4lrrs1n.

For very small angles the sine may be considered as approximately equal to the arc and within limits, say up to 10, the simpler ratio of 22m may be substituted as an equivalent for the more accurate ratio above given and I desire it to be understood that this equivalent also is to be covered by the appended claims.

I claim as my invention: 1. A chart comprising a network produced by two intersecting series of parallel lines, a series of concentric circles, and a the llnes bemg evenly series of radial lines, spaced in each indivldual'serles, and the ratio of the unit interval between said circles to the unit interval between the parallel lines, being equal to 471' Sill.

where 0: indicates the unit of angular subdivision produced by the radial lines.

2. A chart comprising series of straight parallel lines, a series of concentric circles, and a series of radial lines, the ratio of the unit interval between said circles to the unit interval between the parallel lines being equal to 4 where 0: indicates the unit of angular subdivision produced by the radial lines.

41: sin.

3. A chart comprising a series of evenly spaced straight parallel lines, a series of evenly spaced concentric circles, and a series of evenly spaced radial lines, the ratio of the unit interval between the circles to the unit interval between the said parallel lines being equal to a 41: sin.

where 0: indicates the unit of angular subdivision produced by the radial lines.

4. As a new article of manufacture, a chart composed of-a sheet of material having produced thereon a series of straight parallel lines indicating lumens, a series of concentric circles indicating candle power, a series of radial lines forming equal angular subdivisions and a series of radial lines which bisect the angles between each two adjoining radial lines of the first-named series of radial lines, the ratio of the unit interval between the circles to the unit interval between the said parallel lines, being equal to 4?: sin.

where a indicates the unit of angular subdivisions.

In Witness whereof I have hereunto set my hand in the presence of two subscribing witnesses.

. ALFRED A. WOHLAUER.

Witnesses:

J OHN Lorna, JOHN A. KEHLENBECK. 

